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Quantum graphs: PT -symmetry and reflection symmetry of the spectrum
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
2017 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 58, no 2, 023506Article in journal (Refereed) Published
Abstract [en]

Not necessarily self-adjoint quantum graphs-differential operators on metric graphs-are considered. Assume in addition that the underlying metric graph possesses an automorphism (symmetry) P. If the differential operator is PT -symmetric, then its spectrum has reflection symmetry with respect to the real line. Our goal is to understand whether the opposite statement holds, namely, whether the reflection symmetry of the spectrum of a quantum graph implies that the underlying metric graph possesses a non-trivial automorphism and the differential operator is PT symmetric. We give partial answer to this question by considering equilateral stargraphs. The corresponding Laplace operator with Robin vertex conditions possesses reflection-symmetric spectrum if and only if the operator is PT -symmetric with P being an automorphism of the metric graph.

Place, publisher, year, edition, pages
AMER INST PHYSICS , 2017. Vol. 58, no 2, 023506
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-205112DOI: 10.1063/1.4975757ISI: 000395290100029Scopus ID: 2-s2.0-85013167751OAI: oai:DiVA.org:kth-205112DiVA: diva2:1114875
Note

QC 20170626

Available from: 2017-06-26 Created: 2017-06-26 Last updated: 2017-06-26Bibliographically approved

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Garjani, B. Majidzadeh
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